Problem
The common-pool problem in government spending. (Weingarten, Shipley, and Johnson, 1981.) Suppose the economy consists of M > 1 congressional districts. The utility of the representative person living in district i is E +V(Gi)-C (T ). E is the endowment, Gi is the level of a local public good in district i, and T is taxes (which are assumed to be the same in all districts). Assume V (•) > 0, V (•) < 0,="" c ="" (•)=""> 0, and C (•) > 0. The government budget constraint is i=1∑M Gi = MT the representative from each district dictates the values of G in his or her district. Each representative maximizes the utility of the representative person living in his or her district.
(a) Find the first-order condition for the value of Gj chosen by the representative from district j, given the values of Gi chosen by the other representatives and the government budget constraint.
(b) Find the condition for the Nash equilibrium value of G. That is, find the condition for the value of G such that if all other representatives choose that value for their Gi, a given representative wants to choose that value.
(c) Is the Nash equilibrium Pareto-efficient? Explain. What is the intuition for this result?